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Journal of Convex Analysis 28 (2021), No. 1, 143--156
Copyright Heldermann Verlag 2021

Asymptotic Hyers-Ulam Stability or Superstability by Unilateral Perturbations on the Concavity Side for Generalized Linear Equations

Catherine Peppo
Itescia, 8 rue Pierre de Coubertin, 95300 Pontoise, France


In a recent paper [{\it Asymptotic Hyers-Ulam stability or superstability for generalized linear equations by unilateral perturbations}, J. Convex Analysis 26 (2019) 543--562] we considered in relation to the famous problem of Ulam ``Give conditions in order for a linear mapping near an approximated linear mapping to exist" the stability or superstability of a generalized linear equation $$ {||{f(x+y)-f(x)-f(y)}||=B[\phi(x)+\phi(y)]} $$ by perturbations on the convexity side, named right perturbations. In this paper we continue this research for perturbations on the concavity side with some hypotheses of concavity.

Keywords: Hyers-Ulam stability, superstability, asymptotic stability, linear equation, affine equation, exponential equation.

MSC: 39B62, 26A51.

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